-There is thus a total of 32 configurations, encoded in 5 bits. One bit is used to signal mono vs stereo, which leaves 2 bits for the number of frames per packets (codes 0 to 3):

+The remaining two bits of the TOC byte, labeled "c", code the number of frames

+ per packet (codes 0 to 3) as follows:

<list style="symbols">

<t>0: 1 frame in the packet</t>

<t>1: 2 frames in the packet, each with equal compressed size</t>

-<t>2: 2 frames in the packet, with different compressed size</t>

-<t>3: arbitrary number of frames in the packet</t>

+<t>2: 2 frames in the packet, with different compressed sizes</t>

+<t>3: an arbitrary number of frames in the packet</t>

</list>

-For code 2, the TOC byte is followed by the length of the first frame, encoded as described below.

-For code 3, the TOC byte is followed by a byte encoding the number of frames in the packet, with the MSB indicating VBR. In the VBR case, the byte indicating the number of frames is followed by N-1 frame

-lengths encoded as described below. As an additional limit, the audio duration contained

-within a packet MUST NOT exceed 120 ms.

+This draft refers to a packet as a code 0 packet, code 1 packet, etc., based on

+ the value of "c".

+</t>

+

+</section>

+

+<section title="Frame Packing">

+

+<t>

+This section describes how frames are packed according to each possible value

+ of "c" in the TOC byte.

</t>

+<section anchor="frame-length-coding" title="Frame Length Coding">

<t>

-The compressed size of the frames (if needed) is indicated -- usually -- with one byte, with the following meaning:

+This is handled by coding 8 shell blocks (128 samples) and discarding the final

+ 8 samples of the last block.

+The decoder contains no special case that prevents an encoder from placing

+ pulses in these samples, and they must be correctly parsed from the bitstream

+ if present, but they are otherwise ignored.

+</t>

+

+<texttable anchor="silk_shell_block_table"

+ title="Number of Shell Blocks Per SILK Frame">

+<ttcol>Audio Bandwidth</ttcol>

+<ttcol>Frame Size</ttcol>

+<ttcol align="right">Number of Shell Blocks</ttcol>

+<c>NB</c> <c>10&nbsp;ms</c> <c>5</c>

+<c>MB</c> <c>10&nbsp;ms</c> <c>8</c>

+<c>WB</c> <c>10&nbsp;ms</c> <c>10</c>

+<c>NB</c> <c>20&nbsp;ms</c> <c>10</c>

+<c>MB</c> <c>20&nbsp;ms</c> <c>15</c>

+<c>WB</c> <c>20&nbsp;ms</c> <c>20</c>

+</texttable>

+

+<section anchor="silk_rate_level" title="Rate Level">

+<t>

+The first symbol in the excitation is a "rate level", which is an index from 0

+ to 8, inclusive, coded using the PDF in <xref target="silk_rate_level_pdfs"/>

+ corresponding to the signal type of the current frame (from

+ <xref target="silk_frame_type"/>).

+The rate level selects the PDF used to decode the number of pulses in

+ the individual shell blocks.

+It does not directly convey any information about the bitrate or the number of

+ pulses itself, but merely changes the probability of the symbols in

+ <xref target="silk_pulse_counts"/>.

+Level&nbsp;0 provides a more efficient encoding at low rates generally, and

+ level&nbsp;8 provides a more efficient encoding at high rates generally,

+ though the most efficient level for a particular SILK frame may depend on the

+ exact distribution of the coded symbols.

+An encoder should, but is not required to, use the most efficient rate level.

+</t>

+

+<texttable anchor="silk_rate_level_pdfs"

+ title="PDFs for the Rate Level">

+<ttcol>Signal Type</ttcol>

+<ttcol>PDF</ttcol>

+<c>Inactive or Unvoiced</c>

+<c>{15, 51, 12, 46, 45, 13, 33, 27, 14}/256</c>

+<c>Voiced</c>

+<c>{33, 30, 36, 17, 34, 49, 18, 21, 18}/256</c>

+</texttable>

+

</section>

- <section anchor='outline_decoder' title='SILK Decoder'>

- <t>

- At the receiving end, the received packets are by the range decoder split into a number of frames contained in the packet. Each of which contains the necessary information to reconstruct a 20 ms frame of the output signal.

- </t>

- <section title="Decoder Modules">

- <t>

- An overview of the decoder is given in <xref target="decoder_figure" />.

- <figure align="center" anchor="decoder_figure">

- <artwork align="center">

- <![CDATA[

-

- +---------+ +------------+

--->| Range |--->| Decode |---------------------------+

- 1 | Decoder | 2 | Parameters |----------+ 5 |

- +---------+ +------------+ 4 | |

- 3 | | |

- \/ \/ \/

- +------------+ +------------+ +------------+

- | Generate |-->| LTP |-->| LPC |-->

- | Excitation | | Synthesis | | Synthesis | 6

- +------------+ +------------+ +------------+

+<section anchor="silk_pulse_counts" title="Pulses Per Shell Block">

+<t>

+The total number of pulses in each of the shell blocks follows the rate level.

+The pulse counts for all of the shell blocks are coded consecutively, before

+ the content of any of the blocks.

+Each block may have anywhere from 0 to 16 pulses, inclusive, coded using the

+ 18-entry PDF in <xref target="silk_pulse_count_pdfs"/> corresponding to the

+ rate level from <xref target="silk_rate_level"/>.

+The special value 17 indicates that this block has one or more additional

+ LSBs to decode for each coefficient.

+If the decoder encounters this value, it decodes another value for the actual

+ pulse count of the block, but uses the PDF corresponding to the special rate

+ level&nbsp;9 instead of the normal rate level.

+This process repeats until the decoder reads a value less than 17, and it then

+ sets the number of extra LSBs used to the number of 17's decoded for that

+ block.

+If it reads the value 17 ten times, then the next iteration uses the special

+ rate level&nbsp;10 instead of 9.

+The probability of decoding a 17 when using the PDF for rate level&nbsp;10 is

+ zero, ensuring that the number of LSBs for a block will not exceed 10.

+The cumulative distribution for rate level&nbsp;10 is just a shifted version of

+ that for 9 and thus does not require any additional storage.

+</t>

-1: Range encoded bitstream

-2: Coded parameters

-3: Pulses and gains

-4: Pitch lags and LTP coefficients

-5: LPC coefficients

-6: Decoded signal

-]]>

- </artwork>

- <postamble>Decoder block diagram.</postamble>

- </figure>

- </t>

-

- <section title='Range Decoder'>

- <t>

- The range decoder decodes the encoded parameters from the received bitstream. Output from this function includes the pulses and gains for the excitation signal generation, as well as LTP and LSF codebook indices, which are needed for decoding LTP and LPC coefficients needed for LTP and LPC synthesis filtering the excitation signal, respectively.

- </t>

- </section>

-

- <section title='Decode Parameters'>

- <t>

- Pulses and gains are decoded from the parameters that were decoded by the range decoder.

- </t>

-

- <t>

- When a voiced frame is decoded and LTP codebook selection and indices are received, LTP coefficients are decoded using the selected codebook by choosing the vector that corresponds to the given codebook index in that codebook. This is done for each of the four subframes.

- The LPC coefficients are decoded from the LSF codebook by first adding the chosen vectors, one vector from each stage of the codebook. The resulting LSF vector is stabilized using the same method that was used in the encoder, see

- <xref target='lsf_stabilizer_overview_section' />. The LSF coefficients are then converted to LPC coefficients, and passed on to the LPC synthesis filter.

- </t>

- </section>

-

- <section title='Generate Excitation'>

- <t>

- The pulses signal is multiplied with the quantization gain to create the excitation signal.

- </t>

- </section>

-

- <section title='LTP Synthesis'>

- <t>

- For voiced speech, the excitation signal e(n) is input to an LTP synthesis filter that will recreate the long term correlation that was removed in the LTP analysis filter and generate an LPC excitation signal e_LPC(n), according to

- For unvoiced speech, the output signal is simply a copy of the excitation signal, i.e., e_LPC(n) = e(n).

- </t>

- </section>

+</section>

- <section title='LPC Synthesis'>

- <t>

- In a similar manner, the short-term correlation that was removed in the LPC analysis filter is recreated in the LPC synthesis filter. The LPC excitation signal e_LPC(n) is filtered using the LTP coefficients a_i, according to

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- d_LPC

- __

-y(n) = e_LPC(n) + \ e_LPC(n - i) * a_i,

- /_

- i=1

-]]>

- </artwork>

- </figure>

- where d_LPC is the LPC synthesis filter order, and y(n) is the decoded output signal.

- In the following, we focus on the core encoder and describe its components. For simplicity, we will refer to the core encoder simply as the encoder in the remainder of this document. An overview of the encoder is given in <xref target="encoder_figure" />.

- </t>

-

- <figure align="center" anchor="encoder_figure">

- <artwork align="center">

- <![CDATA[

- +---+

- +----------------------------->| |

- +---------+ | +---------+ | |

- |Voice | | |LTP | | |

- +----->|Activity |-----+ +---->|Scaling |---------+--->| |

- | |Detector | 3 | | |Control |<+ 12 | | |

- | +---------+ | | +---------+ | | | |

- | | | +---------+ | | | |

- | | | |Gains | | 11 | | |

- | | | +->|Processor|-|---+---|--->| R |

- | | | | | | | | | | a |

- | \/ | | +---------+ | | | | n |

- | +---------+ | | +---------+ | | | | g |

- | |Pitch | | | |LSF | | | | | e |

- | +->|Analysis |-+ | |Quantizer|-|---|---|--->| |

- | | | |4| | | | | 8 | | | E |->

- | | +---------+ | | +---------+ | | | | n |14

- | | | | 9/\ 10| | | | | c |

- | | | | | \/ | | | | o |

- | | +---------+ | | +----------+| | | | d |

- | | |Noise | +--|->|Prediction|+---|---|--->| e |

- | +->|Shaping |-|--+ |Analysis || 7 | | | r |

- | | |Analysis |5| | | || | | | |

- | | +---------+ | | +----------+| | | | |

- | | | | /\ | | | | |

- | | +---------|--|-------+ | | | | |

- | | | \/ \/ \/ \/ \/ | |

- | +---------+ | | +---------+ +------------+ | |

- | |High-Pass| | | | | |Noise | | |

--+->|Filter |-+----+----->|Prefilter|------>|Shaping |->| |

-1 | | 2 | | 6 |Quantization|13| |

- +---------+ +---------+ +------------+ +---+

+<section title='SILK Encoder'>

+ <t>

+ In many respects the SILK encoder mirrors the SILK decoder described

+ in <xref target='silk_decoder_outline'/>.

+ Details such as the quantization and range coder tables can be found

+ there, while this section describes the high-level design choices that

- The input signal is processed by a VAD (Voice Activity Detector) to produce a measure of voice activity, and also spectral tilt and signal-to-noise estimates, for each frame. The VAD uses a sequence of half-band filterbanks to split the signal in four subbands: 0 - Fs/16, Fs/16 - Fs/8, Fs/8 - Fs/4, and Fs/4 - Fs/2, where Fs is the sampling frequency, that is, 8, 12, 16 or 24 kHz. The lowest subband, from 0 - Fs/16 is high-pass filtered with a first-order MA (Moving Average) filter (with transfer function H(z) = 1-z^(-1)) to reduce the energy at the lowest frequencies. For each frame, the signal energy per subband is computed. In each subband, a noise level estimator tracks the background noise level and an SNR (Signal-to-Noise Ratio) value is computed as the logarithm of the ratio of energy to noise level. Using these intermediate variables, the following parameters are calculated for use in other SILK modules:

- <list style="symbols">

- <t>

- Average SNR. The average of the subband SNR values.

- </t>

-

- <t>

- Smoothed subband SNRs. Temporally smoothed subband SNR values.

- </t>

-

- <t>

- Speech activity level. Based on the average SNR and a weighted average of the subband energies.

- </t>

-

- <t>

- Spectral tilt. A weighted average of the subband SNRs, with positive weights for the low subbands and negative weights for the high subbands.

- </t>

- </list>

- </t>

- </section>

-

- <section title='High-Pass Filter'>

- <t>

- The input signal is filtered by a high-pass filter to remove the lowest part of the spectrum that contains little speech energy and may contain background noise. This is a second order ARMA (Auto Regressive Moving Average) filter with a cut-off frequency around 70 Hz.

- </t>

- <t>

- In the future, a music detector may also be used to lower the cut-off frequency when the input signal is detected to be music rather than speech.

- The pitch analysis finds a binary voiced/unvoiced classification, and, for frames classified as voiced, four pitch lags per frame - one for each 5 ms subframe - and a pitch correlation indicating the periodicity of the signal. The input is first whitened using a Linear Prediction (LP) whitening filter, where the coefficients are computed through standard Linear Prediction Coding (LPC) analysis. The order of the whitening filter is 16 for best results, but is reduced to 12 for medium complexity and 8 for low complexity modes. The whitened signal is analyzed to find pitch lags for which the time correlation is high. The analysis consists of three stages for reducing the complexity:

- <list style="symbols">

- <t>In the first stage, the whitened signal is downsampled to 4 kHz (from 8 kHz) and the current frame is correlated to a signal delayed by a range of lags, starting from a shortest lag corresponding to 500 Hz, to a longest lag corresponding to 56 Hz.</t>

-

- <t>

- The second stage operates on a 8 kHz signal ( downsampled from 12, 16 or 24 kHz ) and measures time correlations only near the lags corresponding to those that had sufficiently high correlations in the first stage. The resulting correlations are adjusted for a small bias towards short lags to avoid ending up with a multiple of the true pitch lag. The highest adjusted correlation is compared to a threshold depending on:

- <list style="symbols">

- <t>

- Whether the previous frame was classified as voiced

- </t>

- <t>

- The speech activity level

- </t>

- <t>

- The spectral tilt.

- </t>

- </list>

- If the threshold is exceeded, the current frame is classified as voiced and the lag with the highest adjusted correlation is stored for a final pitch analysis of the highest precision in the third stage.

- </t>

- <t>

- The last stage operates directly on the whitened input signal to compute time correlations for each of the four subframes independently in a narrow range around the lag with highest correlation from the second stage.

- The noise shaping analysis finds gains and filter coefficients used in the prefilter and noise shaping quantizer. These parameters are chosen such that they will fulfil several requirements:

- <list style="symbols">

- <t>Balancing quantization noise and bitrate. The quantization gains determine the step size between reconstruction levels of the excitation signal. Therefore, increasing the quantization gain amplifies quantization noise, but also reduces the bitrate by lowering the entropy of the quantization indices.</t>

- <t>Spectral shaping of the quantization noise; the noise shaping quantizer is capable of reducing quantization noise in some parts of the spectrum at the cost of increased noise in other parts without substantially changing the bitrate. By shaping the noise such that it follows the signal spectrum, it becomes less audible. In practice, best results are obtained by making the shape of the noise spectrum slightly flatter than the signal spectrum.</t>

- <t>Deemphasizing spectral valleys; by using different coefficients in the analysis and synthesis part of the prefilter and noise shaping quantizer, the levels of the spectral valleys can be decreased relative to the levels of the spectral peaks such as speech formants and harmonics. This reduces the entropy of the signal, which is the difference between the coded signal and the quantization noise, thus lowering the bitrate.</t>

- <t>Matching the levels of the decoded speech formants to the levels of the original speech formants; an adjustment gain and a first order tilt coefficient are computed to compensate for the effect of the noise shaping quantization on the level and spectral tilt.</t>

- <xref target='noise_shape_analysis_spectra_figure' /> shows an example of an input signal spectrum (1). After de-emphasis and level matching, the spectrum has deeper valleys (2). The quantization noise spectrum (3) more or less follows the input signal spectrum, while having slightly less pronounced peaks. The entropy, which provides a lower bound on the bitrate for encoding the excitation signal, is proportional to the area between the deemphasized spectrum (2) and the quantization noise spectrum (3). Without de-emphasis, the entropy is proportional to the area between input spectrum (1) and quantization noise (3) - clearly higher.

- </t>

+</artwork>

+</figure>

+<xref target='noise_shape_analysis_spectra_figure' /> shows an example of an

+The quantization noise spectrum (3) more or less follows the input signal

+spectrum, while having slightly less pronounced peaks.

+The entropy, which provides a lower bound on the bitrate for encoding the

+excitation signal, is proportional to the area between the de-emphasized

+spectrum (2) and the quantization noise spectrum (3). Without de-emphasis,

+the entropy is proportional to the area between input spectrum (1) and

+quantization noise (3) - clearly higher.

+</t>

- <t>

- The transformation from input signal to deemphasized signal can be described as a filtering operation with a filter

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- Wana(z)

-H(z) = G * ( 1 - c_tilt * z^(-1) ) * -------

- Wsyn(z),

- ]]>

- </artwork>

- </figure>

- having an adjustment gain G, a first order tilt adjustment filter with

- tilt coefficient c_tilt, and where

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- 16 d

- __ __

-Wana(z) = (1 - \ (a_ana(k) * z^(-k))*(1 - z^(-L) \ b_ana(k)*z^(-k)),

- /_ /_

- k=1 k=-d

- ]]>

- </artwork>

- </figure>

- is the analysis part of the de-emphasis filter, consisting of the short-term shaping filter with coefficients a_ana(k), and the long-term shaping filter with coefficients b_ana(k) and pitch lag L. The parameter d determines the number of long-term shaping filter taps.

- </t>

+<t>

+The transformation from input signal to de-emphasized signal can be

+described as a filtering operation with a filter

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+ -1 Wana(z)

+H(z) = G * ( 1 - c_tilt * z ) * -------

+ Wsyn(z),

+]]>

+</artwork>

+</figure>

+having an adjustment gain G, a first order tilt adjustment filter with

+tilt coefficient c_tilt, and where

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+ 16 d

+ __ -k -L __ -k

+Wana(z) = (1 - \ (a_ana(k) * z )*(1 - z * \ b_ana(k) * z ),

+ /_ /_

+ k=1 k=-d

+]]>

+</artwork>

+</figure>

+is the analysis part of the de-emphasis filter, consisting of the short-term

+shaping filter with coefficients a_ana(k), and the long-term shaping filter

- Similarly, but without the tilt adjustment, the synthesis part can be written as

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- 16 d

- __ __

-Wsyn(z) = (1 - \ (a_syn(k) * z^(-k))*(1 - z^(-L) \ b_syn(k)*z^(-k)).

- /_ /_

- k=1 k=-d

- ]]>

- </artwork>

- </figure>

- </t>

- <t>

- All noise shaping parameters are computed and applied per subframe of 5 milliseconds. First, an LPC analysis is performed on a windowed signal block of 15 milliseconds. The signal block has a look-ahead of 5 milliseconds relative to the current subframe, and the window is an asymmetric sine window. The LPC analysis is done with the autocorrelation method, with an order of 16 for best quality or 12 in low complexity operation. The quantization gain is found as the square-root of the residual energy from the LPC analysis, multiplied by a value inversely proportional to the coding quality control parameter and the pitch correlation.

- </t>

- <t>

- Next we find the two sets of short-term noise shaping coefficients a_ana(k) and a_syn(k), by applying different amounts of bandwidth expansion to the coefficients found in the LPC analysis. This bandwidth expansion moves the roots of the LPC polynomial towards the origo, using the formulas

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- a_ana(k) = a(k)*g_ana^k, and

- a_syn(k) = a(k)*g_syn^k,

- ]]>

- </artwork>

- </figure>

- where a(k) is the k'th LPC coefficient and the bandwidth expansion factors g_ana and g_syn are calculated as

- <figure align="center">

- <artwork align="center">

- <![CDATA[

-g_ana = 0.94 - 0.02*C, and

-g_syn = 0.94 + 0.02*C,

+<t>

+Similarly, but without the tilt adjustment, the synthesis part can be written as

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+ 16 d

+ __ -k -L __ -k

+Wsyn(z) = (1 - \ (a_syn(k) * z )*(1 - z * \ b_syn(k) * z ).

+ /_ /_

+ k=1 k=-d

]]>

- </artwork>

- </figure>

- where C is the coding quality control parameter between 0 and 1. Applying more bandwidth expansion to the analysis part than to the synthesis part gives the desired de-emphasis of spectral valleys in between formants.

- </t>

+</artwork>

+</figure>

+</t>

+<t>

+All noise shaping parameters are computed and applied per subframe of 5&nbsp;ms.

+First, an LPC analysis is performed on a windowed signal block of 15&nbsp;ms.

+The signal block has a look-ahead of 5&nbsp;ms relative to the current subframe,

+and the window is an asymmetric sine window. The LPC analysis is done with the

+autocorrelation method, with an order of between 8, in lowest-complexity mode,

+and 16, for best quality.

+</t>

+<t>

+Optionally the LPC analysis and noise shaping filters are warped by replacing

+the delay elements by first-order allpass filters.

+This increases the frequency resolution at low frequencies and reduces it at

+high ones, which better matches the human auditory system and improves

+quality.

+The warped analysis and filtering comes at a cost in complexity

+and is therefore only done in higher complexity modes.

+</t>

+<t>

+The quantization gain is found by taking the square root of the residual energy

+from the LPC analysis and multiplying it by a value inversely proportional

+to the coding quality control parameter and the pitch correlation.

+</t>

+<t>

+Next the two sets of short-term noise shaping coefficients a_ana(k) and

+a_syn(k) are obtained by applying different amounts of bandwidth expansion to the

+coefficients found in the LPC analysis.

+This bandwidth expansion moves the roots of the LPC polynomial towards the

+origin, using the formulas

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+ k

+ a_ana(k) = a(k)*g_ana , and

- <t>

- The long-term shaping is applied only during voiced frames. It uses three filter taps, described by

- <figure align="center">

- <artwork align="center">

- <![CDATA[

+ k

+ a_syn(k) = a(k)*g_syn ,

+]]>

+</artwork>

+</figure>

+where a(k) is the k'th LPC coefficient, and the bandwidth expansion factors

+g_ana and g_syn are calculated as

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+g_ana = 0.95 - 0.01*C, and

+

+g_syn = 0.95 + 0.01*C,

+]]>

+</artwork>

+</figure>

+where C is the coding quality control parameter between 0 and 1.

+Applying more bandwidth expansion to the analysis part than to the synthesis

+part gives the desired de-emphasis of spectral valleys in between formants.

+</t>

+

+<t>

+The long-term shaping is applied only during voiced frames.

+It uses three filter taps, described by

+<figure align="center">

+<artwork align="center">

+ <![CDATA[

b_ana = F_ana * [0.25, 0.5, 0.25], and

-b_syn = F_syn * [0.25, 0.5, 0.25].

- ]]>

- </artwork>

- </figure>

- For unvoiced frames these coefficients are set to 0. The multiplication factors F_ana and F_syn are chosen between 0 and 1, depending on the coding quality control parameter, as well as the calculated pitch correlation and smoothed subband SNR of the lowest subband. By having F_ana less than F_syn, the pitch harmonics are emphasized relative to the valleys in between the harmonics.

- </t>

- <t>

- The tilt coefficient c_tilt is for unvoiced frames chosen as

- <figure align="center">

- <artwork align="center">

- <![CDATA[

-c_tilt = 0.4, and as

-c_tilt = 0.04 + 0.06 * C

- ]]>

- </artwork>

- </figure>

- for voiced frames, where C again is the coding quality control parameter and is between 0 and 1.

- </t>

- <t>

- The adjustment gain G serves to correct any level mismatch between original and decoded signal that might arise from the noise shaping and de-emphasis. This gain is computed as the ratio of the prediction gain of the short-term analysis and synthesis filter coefficients. The prediction gain of an LPC synthesis filter is the square-root of the output energy when the filter is excited by a unit-energy impulse on the input. An efficient way to compute the prediction gain is by first computing the reflection coefficients from the LPC coefficients through the step-down algorithm, and extracting the prediction gain from the reflection coefficients as

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- K

- ___

- predGain = ( | | 1 - (r_k)^2 )^(-0.5),

- k=1

- ]]>

- </artwork>

- </figure>

- where r_k is the k'th reflection coefficient.

- </t>

-

- <t>

- Initial values for the quantization gains are computed as the square-root of the residual energy of the LPC analysis, adjusted by the coding quality control parameter. These quantization gains are later adjusted based on the results of the prediction analysis.

- </t>

- </section>

-

- <section title='Prefilter'>

- <t>

- In the prefilter the input signal is filtered using the spectral valley de-emphasis filter coefficients from the noise shaping analysis, see <xref target='noise_shaping_analysis_overview_section' />. By applying only the noise shaping analysis filter to the input signal, it provides the input to the noise shaping quantizer.

- The prediction analysis is performed in one of two ways depending on how the pitch estimator classified the frame. The processing for voiced and unvoiced speech are described in <xref target='pred_ana_voiced_overview_section' /> and <xref target='pred_ana_unvoiced_overview_section' />, respectively. Inputs to this function include the pre-whitened signal from the pitch estimator, see <xref target='pitch_estimator_overview_section' />.

- For a frame of voiced speech the pitch pulses will remain dominant in the pre-whitened input signal. Further whitening is desirable as it leads to higher quality at the same available bit-rate. To achieve this, a Long-Term Prediction (LTP) analysis is carried out to estimate the coefficients of a fifth order LTP filter for each of four sub-frames. The LTP coefficients are used to find an LTP residual signal with the simulated output signal as input to obtain better modelling of the output signal. This LTP residual signal is the input to an LPC analysis where the LPCs are estimated using Burgs method, such that the residual energy is minimized. The estimated LPCs are converted to a Line Spectral Frequency (LSF) vector, and quantized as described in <xref target='lsf_quantizer_overview_section' />. After quantization, the quantized LSF vector is converted to LPC coefficients and hence by using these quantized coefficients the encoder remains fully synchronized with the decoder. The LTP coefficients are quantized using a method described in <xref target='ltp_quantizer_overview_section' />. The quantized LPC and LTP coefficients are now used to filter the high-pass filtered input signal and measure a residual energy for each of the four subframes.

- For a speech signal that has been classified as unvoiced there is no need for LTP filtering as it has already been determined that the pre-whitened input signal is not periodic enough within the allowed pitch period range for an LTP analysis to be worth-while the cost in terms of complexity and rate. Therefore, the pre-whitened input signal is discarded and instead the high-pass filtered input signal is used for LPC analysis using Burgs method. The resulting LPC coefficients are converted to an LSF vector, quantized as described in the following section and transformed back to obtain quantized LPC coefficients. The quantized LPC coefficients are used to filter the high-pass filtered input signal and measure a residual energy for each of the four subframes.

- <t>The purpose of quantization in general is to significantly lower the bit rate at the cost of some introduced distortion. A higher rate should always result in lower distortion, and lowering the rate will generally lead to higher distortion. A commonly used but generally sub-optimal approach is to use a quantization method with a constant rate where only the error is minimized when quantizing.</t>

- <section title='Rate-Distortion Optimization'>

- <t>Instead, we minimize an objective function that consists of a weighted sum of rate and distortion, and use a codebook with an associated non-uniform rate table. Thus, we take into account that the probability mass function for selecting the codebook entries are by no means guaranteed to be uniform in our scenario. The advantage of this approach is that it ensures that rarely used codebook vector centroids, which are modelling statistical outliers in the training set can be quantized with a low error but with a relatively high cost in terms of a high rate. At the same time this approach also provides the advantage that frequently used centroids are modelled with low error and a relatively low rate. This approach will lead to equal or lower distortion than the fixed rate codebook at any given average rate, provided that the data is similar to the data used for training the codebook.</t>

- Instead of minimizing the error in the LSF domain, we map the errors to better approximate spectral distortion by applying an individual weight to each element in the error vector. The weight vectors are calculated for each input vector using the Inverse Harmonic Mean Weighting (IHMW) function proposed by Laroia et al., see <xref target="laroia-icassp" />.

- Consequently, we solve the following minimization problem, i.e.,

- <figure align="center">

- <artwork align="center">

- <![CDATA[

-LSF_q = argmin { (LSF - c)' * W * (LSF - c) + mu * rate },

- c in C

- ]]>

- </artwork>

- </figure>

- where LSF_q is the quantized vector, LSF is the input vector to be quantized, and c is the quantized LSF vector candidate taken from the set C of all possible outcomes of the codebook.

- </t>

- </section>

- <section title='Multi-Stage Vector Codebook'>

- <t>

- We arrange the codebook in a multiple stage structure to achieve a quantizer that is both memory efficient and highly scalable in terms of computational complexity, see e.g. <xref target="sinervo-norsig" />. In the first stage the input is the LSF vector to be quantized, and in any other stage s > 1, the input is the quantization error from the previous stage, see <xref target='lsf_quantizer_structure_overview_figure' />.

+For unvoiced frames these coefficients are set to 0. The multiplication factors

+F_ana and F_syn are chosen between 0 and 1, depending on the coding quality

+control parameter, as well as the calculated pitch correlation and smoothed

+subband SNR of the lowest subband. By having F_ana less than F_syn,

+the pitch harmonics are emphasized relative to the valleys in between the

+harmonics.

+</t>

+

+<t>

+The tilt coefficient c_tilt is for unvoiced frames chosen as

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+c_tilt = 0.25,

]]>

- </artwork>

- </figure>

- where M_s is the number of vectors in stage s, we obtain a total of

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- S

- ___

-T = | | Ms

- s=1

+</artwork>

+</figure>

+and as

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+c_tilt = 0.25 + 0.2625 * V

]]>

- </artwork>

- </figure>

- possible combinations for generating the quantized vector. It is for example possible to represent 2^36 uniquely combined vectors using only 216 vectors in memory, as done in SILK for voiced speech at all sample frequencies above 8 kHz.

- </t>

- </section>

- <section title='Survivor Based Codebook Search'>

- <t>

- This number of possible combinations is far too high for a full search to be carried out for each frame so for all stages but the last, i.e., s smaller than S, only the best min( L, Ms ) centroids are carried over to stage s+1. In each stage the objective function, i.e., the weighted sum of accumulated bit-rate and distortion, is evaluated for each codebook vector entry and the results are sorted. Only the best paths and the corresponding quantization errors are considered in the next stage. In the last stage S the single best path through the multistage codebook is determined. By varying the maximum number of survivors from each stage to the next L, the complexity can be adjusted in real-time at the cost of a potential increase when evaluating the objective function for the resulting quantized vector. This approach scales all the way between the two extremes, L=1 being a greedy search, and the desirable but infeasible full search, L=T/MS. In fact, a performance almost as good as what can be achieved with the infeasible full search can be obtained at a substantially lower complexity by using this approach, see e.g. <xref target='leblanc-tsap' />.

- <t>If the input is stable, finding the best candidate will usually result in the quantized vector also being stable, but due to the multi-stage approach it could in theory happen that the best quantization candidate is unstable and because of this there is a need to explicitly ensure that the quantized vectors are stable. Therefore we apply a LSF stabilization method which ensures that the LSF parameters are within valid range, increasingly sorted, and have minimum distances between each other and the border values that have been pre-determined as the 0.01 percentile distance values from a large training set.</t>

- </section>

- <section title='Off-Line Codebook Training'>

- <t>

- The vectors and rate tables for the multi-stage codebook have been trained by minimizing the average of the objective function for LSF vectors from a large training set.

- For voiced frames, the prediction analysis described in <xref target='pred_ana_voiced_overview_section' /> resulted in four sets (one set per subframe) of five LTP coefficients, plus four weighting matrices. Also, the LTP coefficients for each subframe are quantized using entropy constrained vector quantization. A total of three vector codebooks are available for quantization, with different rate-distortion trade-offs. The three codebooks have 10, 20 and 40 vectors and average rates of about 3, 4, and 5 bits per vector, respectively. Consequently, the first codebook has larger average quantization distortion at a lower rate, whereas the last codebook has smaller average quantization distortion at a higher rate. Given the weighting matrix W_ltp and LTP vector b, the weighted rate-distortion measure for a codebook vector cb_i with rate r_i is give by

- <figure align="center">

- <artwork align="center">

- <![CDATA[

- RD = u * (b - cb_i)' * W_ltp * (b - cb_i) + r_i,

+</artwork>

+</figure>

+for voiced frames, where V is the voice activity level between 0 and 1.

+</t>

+<t>

+The adjustment gain G serves to correct any level mismatch between the original

+and decoded signals that might arise from the noise shaping and de-emphasis.

+This gain is computed as the ratio of the prediction gain of the short-term

+analysis and synthesis filter coefficients. The prediction gain of an LPC

+synthesis filter is the square root of the output energy when the filter is

+excited by a unit-energy impulse on the input.

+An efficient way to compute the prediction gain is by first computing the

+reflection coefficients from the LPC coefficients through the step-down

+algorithm, and extracting the prediction gain from the reflection coefficients

+as

+<figure align="center">

+<artwork align="center">

+<![CDATA[

+ K

+ ___ 2 -0.5

+ predGain = ( | | 1 - (r_k) ) ,

+ k=1

]]>

- </artwork>

- </figure>

- where u is a fixed, heuristically-determined parameter balancing the distortion and rate. Which codebook gives the best performance for a given LTP vector depends on the weighting matrix for that LTP vector. For example, for a low valued W_ltp, it is advantageous to use the codebook with 10 vectors as it has a lower average rate. For a large W_ltp, on the other hand, it is often better to use the codebook with 40 vectors, as it is more likely to contain the best codebook vector.

- The weighting matrix W_ltp depends mostly on two aspects of the input signal. The first is the periodicity of the signal; the more periodic the larger W_ltp. The second is the change in signal energy in the current subframe, relative to the signal one pitch lag earlier. A decaying energy leads to a larger W_ltp than an increasing energy. Both aspects do not fluctuate very fast which causes the W_ltp matrices for different subframes of one frame often to be similar. As a result, one of the three codebooks typically gives good performance for all subframes. Therefore the codebook search for the subframe LTP vectors is constrained to only allow codebook vectors to be chosen from the same codebook, resulting in a&